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 Subject: Time/velocity question Category: Science > Physics Asked by: yalexa10-ga List Price: \$20.00 Posted: 09 Jul 2006 12:26 PDT Expires: 08 Aug 2006 12:26 PDT Question ID: 744717
 ```Using the position function -16t^2=1000 and Lim s(a)-s(t) t->a a-t If a construction wokrer drops a wrench from a height of 1000ft, when will the wrench hit the ground? At what velocity will the wrench impact the ground?``` Clarification of Question by yalexa10-ga on 09 Jul 2006 12:30 PDT `the position function is 16t^2-1000 and the limit is s(a)-s(t) / a-t`
 ```Hi yalexa10-ga, At the beginning, when t = 0, the position of the wrench is 1000ft above ground. Therefore, the position function would be: s=1000-16t^2 (where 's' is feet above ground level) At the moment of impact, s=0, which gives: 0=1000-16t^2 Rearranging this gives: 16t^2=1000 then: t^2=1000/16 then: t=(1000/16)^0.5 In other words, t equals the square root of 1000/16, or 7.90569 seconds. To find the velocity at impact we consider the velocity to be the limit (as 't' approaches the time of impact 'a') of: v = ( s(a) - s(t) ) / (a-t) Substituting the position function gives: v = ( 1000-16a^2 - (1000-16t^2) ) / (a-t) which is equivalent to: v = (1000 - 16a^2 - 1000 + 16t^2) / (a-t) which is equivalent to: v = 16(t^2-a^2)/(a-t) It is an algebraic identity, true for any 't' and 'a', that t^2-a^2 is equal to (t+a)(t-a), which is equal to -(a+t)(a-t). Substituting this gives: v = 16(a+t)(a-t)/(a-t) The two occurrences of (a-t) cancel out, leaving us with: v = 16(a+t) In the limit, as 't' approaches the time of impact 'a', this is equivalent to v = 16(a+a) Our time of impact is 7.90569 seconds, therefore the velocity at impact must be: 16(7.90569+7.90569) which is 252.982 feet per second. I trust this provides the information you require. If any of the steps are not clear, please request clarification. Regards, eiffel-ga Google Search Strategy: position displacement velocity equations ://www.google.com/search?q=position+displacement+velocity+equations Additional Link: One-dimensional kinematics http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/1DKinTOC.html```